Let f be a differentiable function defined on the closed interval [a,b] and let c be a point in the open interval (a,b) such that


II.f'(x)>0 when a≤x<c

III.f'(x)<0 when c<x<≤b

Which of the following statements must be true?



(C)f(c) is an absolute maximum value of f on [a,b]

(D)f(c) is an absolute minimum value of f on [a,b]

(E)f(x) has a point of inflection at x=c

  1. 👍
  2. 👎
  3. 👁
  1. Consider the function y = -x^2

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus AP

    f is a differentiable function on the interval [0, 1] and g(x) = f(2x). The table below gives values of f ′(x). What is the value of g ′(0.1)? x 0.1 0.2 0.3 0.4 0.5 f ′(x) 1 2 3 –4 5 The answers are: 1 2 4 cannot be

  2. calculus

    Suppose f is a one-to-one, differentiable function and its inverse function f^−1 is also differentiable. One can show, using implicit differentiation (do it!), that (f^−1)′(x)=1 / f′(f^−1(x)) Find (f^−1)′(−6) if

  3. Math11

    Hello, I don't know how to do this, please help. Thank you. 1).Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 5x2 − 3x + 2, [0, 2] Yes, it does not matter if f is continuous or

  4. calculus

    The function f is continuous on the closed interval [0,2] and has values that are given in the table below x = 0| 1 | 2 ____________ f(x) = 1| k | 2 The equation f(x) = 1/2 must have at least two solutions in the interval [0,2] if

  1. Calculus Please Check my answers

    f is a function that is differentiable for all reals. The value of f ′(x) is given for several values of x in the table below. The table: x -8,-3,0,3,8 f'(x)-4,-2,0,4,5 If f ′(x) is always increasing, which statement about

  2. Calculus

    If f(x) is differentiable for the closed interval [−1, 4] such that f(−1) = −3 and f(4) = 12, then there exists a value c, −1< c < 4 such that a)f'(c)=3 b)f'(c)=0 C)f(c)=-15 d)f(c)=3 I understand that you are supposed to

  3. calculus

    A function f is defined on the interval [0,4], and its derivative is e^sinx-2cos3x a. on what interval is f increasing? b. at what value(s) of x does f have a local maxima? c. how many points of inflection does f have? *calculator

  4. Calculus

    1. The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the intervals between those given

  1. calculus

    f (x)={cx+d for x≤2 {-x^2−cx for x>2 Let f be the function defined above, where c and d are constants. If f is differentiable at x=2, what is the value of c+d ? -4, -2, 0, 2, 4

  2. Calculus

    1. Locate the absolute extrema of the function f(x)=cos(pi*x) on the closed interval [0,1/2]. 2. Determine whether Rolle's Theorem applied to the function f(x)=x^2+6x+8 on the closed interval[-4,-2]. If Rolle's Theorem can be

  3. AP Calculous

    let f be the function defined by f(x)=3X^5 -5X^3 +2 a) on what interval is f increasing? b) on what interval is the graph of f concave upward? c)Write the equation of each horizontal line tangent to the graph of f

  4. Calculus

    The function f is continuous on the closed interval [-5,5], and f(-2) = 6, f(1) = -3, and f(4) = 6. Which of the following statements must be true? A. The equation f(x) = 0 has at least two solutions on the closed interval [-5,5].

You can view more similar questions or ask a new question.